Not a teacher.
Technically, your teacher is correct. In speech, however; it is common for us to shorten things or pronounce them differently to make them easier to say.
"I wouldn't like to do that today."
I might pronounce "wouldn't" similar to "wooden." I might leave out the "t" at the end.
"How are you doing today?"
I would pronounce like:
"Hower ya doin today?"
"There are a lot of people that can help you with your English."
"Therer lots a people that can help you with yer English."
I don't always pronounce the words "correctly," but I am able to communicate to others faster and they all speak similarly. But as a learner of English, I recommend learning to say everything correctly first, then everyone will know what you are trying to say.
Student or Learner